We have been on the Zenith the last two weeks. They had enough towels at the pool, at the whirlpools and we got extra large towels for the beach without signing for them. When you dont bring them back, they ad to you seapass account for it 38 $.
About wine, you have to pay a corkfee (Zenith: 15 $) when you will drink the wine or the champagne in the restaurant during dinner.
We had no problemes get the champagne on board in the handluggage.
Best regards from germany